Question: Simplify to lowest terms. $\dfrac{60}{72}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 60 and 72? $60 = 2\cdot2\cdot3\cdot5$ $72 = 2\cdot2\cdot2\cdot3\cdot3$ $\mbox{GCD}(60, 72) = 2\cdot2\cdot3 = 12$ $\dfrac{60}{72} = \dfrac{5 \cdot 12}{ 6\cdot 12}$ $\hphantom{\dfrac{60}{72}} = \dfrac{5}{6} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{60}{72}} = \dfrac{5}{6} \cdot 1$ $\hphantom{\dfrac{60}{72}} = \dfrac{5}{6}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{60}{72}= \dfrac{2\cdot30}{2\cdot36}= \dfrac{2\cdot 2\cdot15}{2\cdot 2\cdot18}= \dfrac{2\cdot 2\cdot 3\cdot5}{2\cdot 2\cdot 3\cdot6}= \dfrac{5}{6}$